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Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…
In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as shown by Arnold and Hu…
Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…
The irreducible representations of symmetric groups can be realized as certain graded pieces of invariant rings, equivalently as global sections of line bundles on partial flag varieties. There are various ways to choose useful bases of…
In reliability engineering, we need to understand system dependencies, cause-effect relations, identify critical components, and analyze how they trigger failures. Three prominent graph models commonly used for these purposes are fault…
Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…
In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For some fixed $q$, our results can produce more classes of MDS…
In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…
Part III of the reports consists of various unconventional distance function wavelets (DFW). The dimension and the order of partial differential equation (PDE) are first used as a substitute of the scale parameter in the DFW transforms and…
The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but…
A new class of nonparametric nonconforming quadrilateral finite elements is introduced which has the midpoint continuity and the mean value continuity at the interfaces of elements simultaneously as the rectangular DSSY element [J.Douglas,…
Mutually orthogonal complementary sets (MOCSs) and Z-complementary code sets (ZCCSs) have many applications in practical scenarios such as synthetic aperture imaging systems and multi-carrier code division multiple access (MC-CDMA) systems.…
We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the…
Dynamic structure factor (DSF) is important for understanding excitations in many-body physics; it reveals information about the spectral and spatial correlations of fluctuations in quantum systems. Collective phenomena like quantum phase…
New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…
Six-dimensional superconformal field theories (SCFTs) have an atomic classification in terms of elementary building blocks, conformal systems that generalize matter and can be fused together to form all known 6d SCFTs in terms of…
By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and…
We use the Symmetry Topological Field Theory (SymTFT) to study and classify gapped phases in (2+1)d for a class of categorical symmetries, referred to as being of bosonic type. The SymTFTs for these symmetries are given by twisted and…
This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…